- #1

- 5

- 0

"Show that for all integers a and b, ab(a^2 -b^2)(a^2 +b^2) is divisible by 30."

Now, I am aware that this fails if a=b, but I want to try to prove this if we assume a≠b.

I've reduced it to the equation (a^5)b-a(b^5), which works, and I know that I could pick the smallest two integers (1 and 2) and show that, but I don't know how to show that it exists for every integer. Should I do proof by contradiction?